带演化螺旋的水平集强迫平均曲率流解的渐近增长率

IF 1 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-12-30 DOI:10.1112/blms.13227

Hiroyoshi Mitake, Hung V. Tran

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摘要

在这里，我们研究了一个水平集强迫平均曲率流与演化螺旋和齐次诺伊曼边界条件，出现在晶体生长模型。在强迫项的适当条件下，证明了解是全局Lipschitz解。然后我们研究了解的大时间平均值，并推导出晶体的渐近生长速率。得到了该解的一些大时间行为结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals

Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the solution is globally Lipschitz. We then study the large time average of the solution and deduce the asymptotic growth rate of the crystal. Some large time behavior results of the solution are obtained.

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